Classification of ( <i>v</i> , 5)-configurations for <i>v</i> ≤ 11

Abstract We study ( v , k )-configurations with k = 5, which are combinatorial objects. We prove necessary and sufficient conditions for combinatorial equivalence of ( v , 5)-configurations constructed from digraphs with two input and two output arcs in each vertex. We develop an algorithms for construction of ( v , 5)-configurations and identification of combinatorially equivalent of ( v , 5)-configurations. We also give a description of all ( v , 5)-configurations for v ≤ 10 and evaluate the number of combinatorially nonequivalent (11, 5)-configurations.